Raising Rivals Cost to Lessen Competition - GAME THEORY An incumbent earns monopoly prots of $200 if no other rms enter the market. However, if a rival enters the market, the competition that ensues reduces the incumbents prot to $70, with the entrant also earning $70. Since the entrant earns zero if it does not enter but earns $70 by entering, the monopolist will be unable to sustain its monopoly prot unless it can successfully change the business environment. Suppose the incumbent can lobby for a regulation requiring any rm operating in the market (including itself) to obtain a license from the government that costs $90. The incumbent will raise its own xed cost by $90, but more importantly it could also raise its rival's cost by $90. Therefore, the incumbent has two strategies: support a $90 license fee, or do not support it. The potential entrant gets to observe whether there is a license fee before making its entry decision. In the absence of a license fee, if the entrant enters, each rm makes $70 prot. If the entrant stays out of the market, the incumbent enjoys monopoly prots of $200, and the entrant earns $0 by not entering. If the incumbent supports the $90 license fee, and the rival enters the market, they both lose $20 ($70 - $90). If the rival does not enter the market, the resulting prots for the incumbent are $110 (the original $200 monopoly prot less the $90 license fee). The entrant earns $0 by not entering. a. Fill in the blanks in the following payoff matrix.The top number in each quadrant goes to the rival. (4 points) Rival Incumbent Don't Enter $90 License Fee No license b. Analyze this sequential dynamic game in an extensive form diagram or game tree, what is the equilibrium of this game? Find the sub-game perfect Nash equilibrium (where players' strategies are Nash Equilibrium in every sub-game). (5 points) c. Does it make sense for the incumbent to lobby the government for the license fee? Explain. (5 Points)